Determining the absolute neutrino mass scale and the neutrino mass hierarchy are central goals in particle physics, with important implications for the Standard Model. However, the final answer may come from cosmology, as laboratory experiments provide measurements for two of the squared mass dif- ferences and a stringent lower bound on the total neutrino mass - but the upper bound is still poorly constrained, even when considering forecasted results from future probes. Cosmological tracers are very sensitive to neutrino properties and their total mass, because massive neutrinos produce a specific redshift- and scale-dependent signature in the power spectrum of the matter and galaxy distributions. Stringent upper limits on P m will be essential for understanding the neutrino sector, and will nicely complement particle physics results. To this end, we describe here a series of cosmological hydrodynamical simulations which include massive neutrinos, specifically designed to meet the requirements of the Baryon Acous- tic Spectroscopic Survey (BOSS) and focused on the Lyman-α (Lyα) forest - also a useful theoretical ground for upcoming surveys such as SDSS-IV/eBOSS and DESI. We then brie y highlight the remark- able constraining power of the Lyα forest in terms of the total neutrino mass, when combined with other state-of-the-art cosmological probes, leading to a stringent upper bound on ∑mv.

We present two large cosmological N-body simulations, called Horizon Run 2 (HR2) and Horizon Run 3 (HR3), made using 60003 = 216 billions and 72103 = 374 billion particles, spanning a volume of (7.200 h-1Gpc)3 and (10.815 h-1Gpc)3, respectively. These simulations improve on our previous Horizon Run 1 (HR1) up to a factor of 4.4 in volume, and range from 2600 to over 8800 times the volume of the Millennium Run. In addition, they achieve a considerably finer mass resolution, down to 1.25 X 1011h-1M⊙, allowing to resolve galaxy-size halos with mean particle separations of 1.2h-1Mpc and 1.5h-1Mpc, respectively. We have measured the power spectrum, correlation function, mass function and basic halo properties with percent level accuracy, and verified that they correctly reproduce the CDM theoretical expectations, in excellent agreement with linear perturbation theory. Our unprecedentedly large-volume N-body simulations can be used for a variety of studies in cosmology and astrophysics, ranging from large-scale structure topology, baryon acoustic oscillations, dark energy and the characterization of the expansion history of the Universe, till galaxy formation science - in connection with the new SDSS-III. To this end, we made a total of 35 all-sky mock surveys along the past light cone out to z = 0.7 (8 from the HR2 and 27 from the HR3), to simulate the BOSS geometry. The simulations and mock surveys are already publicly available at http://astro.kias.re.kr/Horizon-Run23/.